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  1. On the Necessity of Entanglement for the Explanation of Quantum Speedup.Michael Cuffaro - manuscript
    Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I (...)
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  2. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  3. To Balance a Pencil on its Tip: On the Passive Approach to Quantum Error Correction.Amit Hagar - manuscript
    Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists (...)
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  4. Fidelity and Mistaken Identity for Symplectic Quantum States.Andreas Henriksson - manuscript
    The distinguishability between pairs of quantum states, as measured by quantum fidelity, is formulated on phase space. The fidelity is physically interpreted as the probability that the pair are mistaken for each other upon an measurement. The mathematical representation is based on the concept of symplectic capacity in symplectic topology. The fidelity is the absolute square of the complex-valued overlap between the symplectic capacities of the pair of states. The symplectic capacity for a given state, onto any conjugate plane of (...)
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  5. Quantum Superpositions and the Measurement Problem.Andreas Henriksson - manuscript
    The measurement problem is addressed from the viewpoint that it is the distinguishability between the state preparation and its quantum ensemble, i.e. the set of states with which it has a non-zero overlap, that is at the heart of the difference between classical and quantum measurements. The measure for the degree of distinguishability between pairs of quantum states, i.e. the quantum fidelity, is for this purpose generalized, by the application of the superposition principle, to the setting where there exists an (...)
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  6. Putting Probabilities First. How Hilbert Space Generates and Constrains Them.Michael Janas, Michael Cuffaro & Michel Janssen - manuscript
    We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...)
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  7. Quantum Mechanics Foundations.Bakytzhan Oralbekov - manuscript
    Gravity remains the most elusive field. Its relationship with the electromagnetic field is poorly understood. Relativity and quantum mechanics describe the aforementioned fields, respectively. Bosons and fermions are often credited with responsibility for the interactions of force and matter. It is shown here that fermions factually determine the gravitational structure of the universe, while bosons are responsible for the three established and described forces. Underlying the relationships of the gravitational and electromagnetic fields is a symmetrical probability distribution of fermions and (...)
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  8. Systems with Single Degree of Freedom and the Interpretation of Quantum Mechanics.Mehran Shaghaghi - manuscript
    Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this limitation we demonstrate that such (...)
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  9. The Communicational Properties of Single Photons Explain Their Strange Behavior in the Double-Slit Experiment.Mehran Shaghaghi - manuscript
    Simultaneous observation of the wave-like and particle-like aspects of the photon in the double-slit experiment is unallowed. The underlying reason behind this limitation is not understood. In this paper, we explain this unique behavior by considering the communicational properties of the photons. Photons have three independently adjustable properties (energy, direction, and spin) that can be used to communicate messages. The double-slit experiment setup fixes two of these properties and confines the single photon’s capacity for conveying messages to no more than (...)
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  10. “Quantum Teleportation” and Other Quantum Misnomers.Dieter Zeh - manuscript
  11. A New Problem for Quantum Mechanics.Alexander Meehan - forthcoming - British Journal for the Philosophy of Science:000-000.
    In this article I raise a new problem for quantum mechanics, which I call the control problem. Like the measurement problem, the control problem places a fundamental constraint on quantum theories. The characteristic feature of the problem is its focus on state preparation. In particular, whereas the measurement problem turns on a premise about the completeness of the quantum state ('no hidden variables'), the control problem turns on a premise about our ability to prepare or control quantum states. After raising (...)
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  12. From Quantum Entanglement to Spatiotemporal Distance.Alyssa Ney - forthcoming - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime. Oxford:
    Within the field of quantum gravity, there is an influential research program developing the connection between quantum entanglement and spatiotemporal distance. Quantum information theory gives us highly refined tools for quantifying quantum entanglement such as the entanglement entropy. Through a series of well-confirmed results, it has been shown how these facts about the entanglement entropy of component systems may be connected to facts about spatiotemporal distance. Physicists are seeing these results as yielding promising methods for better understanding the emergence of (...)
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  13. The generalization of the Periodic table. The "Periodic table" of dark matter.Vasil Penchev - 2021 - Computational and Theoretical Chemistry eJournal (Elsevier: SSRN) 4 (4):1-12.
    The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system (...)
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  14. Information Causality, the Tsirelson Bound, and the ‘Being-Thus’ of Things.Michael E. Cuffaro - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72:266-277.
    The principle of 'information causality' can be used to derive an upper bound---known as the 'Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. In this paper, however, I argue that the principle has not to date been sufficiently motivated to play this role; the motivations that have so far been given are either unsatisfactorily vague or else amount to little more than an appeal to intuition. I then consider how (...)
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  15. Quantum Theory is Not Only About Information.Laura Felline - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72:256-265.
    In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that (...)
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  16. Quantum Information Theoretic Approach to the Mind–Brain Problem.Danko D. Georgiev - 2020 - Progress in Biophysics and Molecular Biology 158:16-32.
    The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...)
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  17. Quantum Gravity As the Unification of General Relativity & Quantum Mechanics.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (32):1-3.
    A nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the in-variance “within – out of” of the same system.
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  18. A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory.Vasil Penchev - 2020 - Information Theory and Research eJournal 1 (15):1-13.
    A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section I. (...)
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  19. Atomism in Quantum Mechanics and Information.Vasil Penchev - 2020 - Metaphysics eJournal (Elsevier: SSRN) 13 (12):1-11.
    The original conception of atomism suggests “atoms”, which cannot be divided more into composing parts. However, the name “atom” in physics is reserved for entities, which can be divided into electrons, protons, neutrons and other “elementary particles”, some of which are in turn compounded by other, “more elementary” ones. Instead of this, quantum mechanics is grounded on the actually indivisible quanta of action limited by the fundamental Planck constant. It resolves the problem of how both discrete and continuous (even smooth) (...)
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  20. The Identity of Logic and the World in Terms of Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (21):1-4.
    One can construct a mapping between Hilbert space and the class of all logic if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. Thus that mapping establishes (...)
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  21. Natural Argument by a Quantum Computer.Vasil Penchev - 2020 - Computing Methodology eJournal (Elsevier: SSRN) 3 (30):1-8.
    Natural argument is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary natural arguments in any data. That ability of natural argument is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain quite (...)
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  22. Two Deductions: (1) From the Totality to Quantum Information Conservation; (2) From the Latter to Dark Matter and Dark Energy.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (28):1-47.
    The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive (...)
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  23. Indeterminism in Quantum Mechanics: Beyond and/or Within.Vasil Penchev - 2020 - Development of Innovation eJournal (Elsevier: SSRN) 8 (68):1-5.
    The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical (...)
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  24. Quantum Invariance.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (22):1-6.
    Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to (...)
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  25. A Model of Causal and Probabilistic Reasoning in Frame Semantics.Vasil Penchev - 2020 - Semantics eJournal (Elsevier: SSRN) 2 (18):1-4.
    Quantum mechanics admits a “linguistic interpretation” if one equates preliminary any quantum state of some whether quantum entity or word, i.e. a wave function interpret-able as an element of the separable complex Hilbert space. All possible Feynman pathways can link to each other any two semantic units such as words or term in any theory. Then, the causal reasoning would correspond to the case of classical mechanics (a single trajectory, in which any next point is causally conditioned), and the probabilistic (...)
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  26. The Quantity of Quantum Information and Its Metaphysics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (18):1-6.
    The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...)
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  27. The Frontier of Time: The Concept of Quantum Information.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (17):1-5.
    The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number of (...)
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  28. Quantum Information as the Information of Infinite Series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...)
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  29. Cognition According to Quantum Information: Three Epistemological Puzzles Solved.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (20):1-15.
    The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum in-variance designates (...)
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  30. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...)
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  31. Natural Cybernetics and Mathematical History: The Principle of Least Choice in History.Vasil Penchev - 2020 - Cultural Anthropology (Elsevier: SSRN) 5 (23):1-44.
    The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “complimentary” (...)
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  32. Time: From the Totality to Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (24):1-14.
    The paper justifies the following theses: The totality can found time if the latter is axiomatically represented by its “arrow” as a well-ordering. Time can found choice and thus information in turn. Quantum information and its units, the quantum bits, can be interpreted as their generalization as to infinity and underlying the physical world as well as the ultimate substance of the world both subjective and objective. Thus a pathway of interpretation between the totality via time, order, choice, and information (...)
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  33. If Quantum Mechanics Is the Solution, What Should the Problem Be?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (32):1-10.
    The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly (...)
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  34. Representation and Reality by Language: How to Make a Home Quantum Computer?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (34):1-14.
    A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano arithmetics having a remarkable (...)
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  35. Cyclic Mechanics: The Principle of Cyclicity.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (16):1-35.
    Cyclic mechanic is intended as a suitable generalization both of quantum mechanics and general relativity apt to unify them. It is founded on a few principles, which can be enumerated approximately as follows: 1. Actual infinity or the universe can be considered as a physical and experimentally verifiable entity. It allows of mechanical motion to exist. 2. A new law of conservation has to be involved to generalize and comprise the separate laws of conservation of classical and relativistic mechanics, and (...)
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  36. What Is Quantum Information? Information Symmetry and Mechanical Motion.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-7.
    The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing (...)
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  37. Physical Entity As Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (35):1-15.
    Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a bit, as well as the quantum information itself (...)
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  38. Reducing Emergence: The Case Studies in Statistic Thermodynamics, General Relativity, and Quantum Mechanics.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (23):1-3.
    The emergent properties are properties referring to a system as a whole, but they do not make sense to its elements or parts being small enough. Furthermore certain emergent properties are reducible to those of elements or relevant parts often. The paper means the special case where the description of the system by means of its emergent properties is much simpler than that of its relevant elements or parts. The concept is investigated by a case study based on statistic thermodynamics, (...)
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  39. Gravity as Entanglement. Entanglement as Gravity.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (30):1-23.
    A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, (...)
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  40. Quantum Complementarity: Both Duality and Opposition.Vasil Penchev - 2020 - Metaphysics eJournal (Elsevier: SSRN) 13 (13):1-6.
    Quantum complementarity is interpreted in terms of duality and opposition. Any two conjugates are considered both as dual and opposite. Thus quantum mechanics introduces a mathematical model of them in an exact and experimental science. It is based on the complex Hilbert space, which coincides with the dual one. The two dual Hilbert spaces model both duality and opposition to resolve unifying the quantum and smooth motions. The model involves necessarily infinity even in any finitely dimensional subspace of the complex (...)
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  41. The Indeterminist Objectivity of Quantum Mechanics Versus the Determinist Subjectivity of Classical Physics.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (18):1-5.
    Indeterminism of quantum mechanics is considered as an immediate corollary from the theorems about absence of hidden variables in it, and first of all, the Kochen – Specker theorem. The base postulate of quantum mechanics formulated by Niels Bohr that it studies the system of an investigated microscopic quantum entity and the macroscopic apparatus described by the smooth equations of classical mechanics by the readings of the latter implies as a necessary condition of quantum mechanics the absence of hidden variables, (...)
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  42. Main Concepts in Philosophy of Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (31):1-4.
    Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present as a choice among infinitely many alternatives, (...)
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  43. Time and Information in the Foundations of Physics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (25):1-12.
    The paper justifies the following theses: The totality can found time if the latter is axiomatically represented by its “arrow” as a well-ordering. Time can found choice and thus information in turn. Quantum information and its units, the quantum bits, can be interpreted as their generalization as to infinity and underlying the physical world as well as the ultimate substance of the world both subjective and objective. Thus a pathway of interpretation between the totality via time, order, choice, and information (...)
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  44. God, Logic, and Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-10.
    Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices (...)
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  45. Quantum-Information Conservation. The Problem About “Hidden Variables”, or the “Conservation of Energy Conservation” in Quantum Mechanics: A Historical Lesson for Future Discoveries.Vasil Penchev - 2020 - Energy Engineering (Energy) eJournal (Elsevier: SSRN) 3 (78):1-27.
    The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...)
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  46. The Isomorphism of Minkowski Space and the Separable Complex Hilbert Space and its Physical Interpretation.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier:SSRN) 13 (31):1-3.
    An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance to (...)
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  47. More Than Impossible: Negative and Complex Probabilities and Their Philosophical Interpretation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (16):1-7.
    A historical review and philosophical look at the introduction of “negative probability” as well as “complex probability” is suggested. The generalization of “probability” is forced by mathematical models in physical or technical disciplines. Initially, they are involved only as an auxiliary tool to complement mathematical models to the completeness to corresponding operations. Rewards, they acquire ontological status, especially in quantum mechanics and its formulation as a natural information theory as “quantum information” after the experimental confirmation the phenomena of “entanglement”. Philosophical (...)
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  48. The Case of Quantum Mechanics Mathematizing Reality: The “Superposition” of Mathematically Modelled and Mathematical Reality: Is There Any Room for Gravity?Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (24):1-15.
    A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as (...)
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  49. General Relativity and Quantum Gravity in Terms of Quantum Measure: A Philosophical Comment.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (17):1-37.
    The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a generalized (...)
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  50. Persistence and Nonpersistence as Complementary Models of Identical Quantum Particles.Philip Goyal - 2019 - New Journal of Physics 21.
    According to our understanding of the everyday physical world, observable phenomena are underpinned by persistent objects that can be reidentified across time by observation of their distinctive properties. This understanding is reflected in classical mechanics, which posits that matter consists of persistent, reidentifiable particles. However, the mathematical symmetrization procedures used to describe identical particles within the quantum formalism have led to the widespread belief that identical quantum particles lack either persistence or reidentifiability. However, it has proved difficult to reconcile these (...)
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